1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pogonyaev
3 years ago
15

Find the inverse laplace transform of: (2 s + 4) / (s - 3)^3

Mathematics
1 answer:
Serhud [2]3 years ago
6 0

Answer:

e^{3t}(2t+5t^{2})

Step-by-step explanation:

L^{-1}[\frac{2s+4}{(s-3)^{3}} ]=

Using the Translation theorem to transform the s-3 to s, that means multiplying by and change s to s+3

Translation theorem:L^{1} [F(s-a)=L^{-1}[F(s)|_{s \to s-a}\\ L^{1} [F(s-a)=e^{at} f(t)

L^{-1}[\frac{2s+4}{(s-3)^{3}} ]=e^{3t} L^{-1}[\frac{2(s+3)+4}{s^{3}} ]

Separate the fraction in a sum:

e^{3t} L^{-1}[\frac{2s+10}{s^{3}} ]=e^{3t} L^{-1}[\frac{2s}{s^{3}}+\frac{10}{s^{3}} ]=e^{3t} (L^{-1}[\frac{2}{s^{2}}]+ L^{-1}[\frac{10}{s^{3}}])

The formula for this is:

L^{-1}[\frac{n!}{s^{n+1}} ]=t^{n}

Modify the expression to match the formula.

e^{3t} (2L^{-1}[\frac{1}{s^{1+1}}]+ \frac{10}{2} L^{-1}[\frac{2}{s^{2+1}}])=e^{3t} (2L^{-1}[\frac{1}{s^{1+1}}]+ 5 L^{-1}[\frac{2}{s^{2+1}}])

Solve

e^{3t} (2L^{-1}[\frac{1}{s^{1+1}}]+ 5 L^{-1}[\frac{2}{s^{2+1}}])=e^{3t}(2t+5t^{2} )

You might be interested in
R + 8 > 21 what is the answer
topjm [15]

Answer:

Step-by-step explanation:

░░░░░▐▀█▀▌░░░░▀█▄░░░

░░░░░▐█▄█▌░░░░░░▀█▄░░

░░░░░░▀▄▀░░░▄▄▄▄▄▀▀░░

░░░░▄▄▄██▀▀▀▀░░░░░░░

░░░█▀▄▄▄█░▀▀░░

░░░▌░▄▄▄▐▌▀▀▀░░ This is Bob

▄░▐░░░▄▄░█░▀▀ ░░

▀█▌░░░▄░▀█▀░▀ ░░ Copy and paste him so he can take over brainly.

░░░░░░░▀███▀█░▄░░

░░░░░░▐▌▀▄▀▄▀▐▄░░

░░░░░░▐▀░░░░░░▐▌░░

░░░░░░█░░░░░░░░█░

6 0
3 years ago
) Today there is a discount of $10 off a purchase of 5 or more concert tickets.
antiseptic1488 [7]

Answer:

Tickets * cost - 10

Step-by-step explanation:

5*cost-10

5 0
3 years ago
What are square numbers
Degger [83]

Square numbers are numbers with an odd number of factors. For example, 1 and 4 are square numbers.

3 0
3 years ago
Explain how the Quotient of Powers Property was used to simplify this expression. three to the fourth power over nine which equa
olga_2 [115]

Answer:

to the fourth power, over 25 = 52 A… Get the answers you need, now! ... B. By simplifying 25 to 52 to make both powers base five and adding the exponents ... was used to simplify the expression is D. By finding the quotient of the ... rules of exponents simplify the expressions below: 2 4 3 0 4 6 4 -3 2 3 2.

Step-by-step explanation:

5 0
3 years ago
Marcella dived 40.8 gallons of paint among 8 coontainer How much paint is in each container
erma4kov [3.2K]

5.1gallons is in each container

3 0
3 years ago
Other questions:
  • Clara visits the aquarium while on vacation.the aquarium is 2and1/2 miles from her hotel.she walks 1/4 mile to bus stop, takes t
    12·2 answers
  • What is the total amount you would pay in a restaurant , if the bill was $70.00, and you first added 8.25% for the tax and then
    10·2 answers
  • How do I figure out what to do in this circle graph/pie chart
    14·1 answer
  • Anyone know this? Please help
    7·2 answers
  • Team A is located on the south bank of a river. Teams B and C are located on the north bank. The angle formed from Team C to Tea
    8·1 answer
  • A science fair poster is a rectangle 3 feet long and 2 feet wide. What is the area of the poster in square inches?
    8·1 answer
  • EASY MATH THAT I DON,T GET PLZ HELP QUICKLY<br>​
    8·1 answer
  • Imagine that you are representing your classmates. What are their needs? What would you advocate for their behalf? Not math rela
    12·1 answer
  • Find 80% of 14,236.<br> Enter the correct answer in the box.
    10·2 answers
  • 11.5 is what percent of 8? Round to the nearest tenth.
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!